Happy New Year, if you are a Celt, a Wiccan, or just someone who feels that this time of year is more evocative of endings and beginnings than 1 January.
I've never really seen the transition from December to January as very new beginning-ish. It is still dark, still cold, still more the thing that was than the thing that is to come. Part of this, I'm sure, is that for nearly all of my life, I have been on an academic calendar, and so the year never runs from January to December. Part of this is because, in the calendar of my religion, these days are the Days of the Dead, the Feasts of All Saints, and All Souls, and this time of remembrance, and saying goodbye, seems to me like what one does at the close of the year. The year should die on the Day of the Dead.
And because, as J.E. Flecker wrote in "The Bridge of Fire," "the wheels of time are turning, turning, turning," this is not just an end but a beginning. Resurrection follows death, and the year begins anew.